Subgroups — #11763888

Order 1088.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×D₁₇	C₂	1	1	yes	maximal, characteristic
2	#10587680	C₂	1	2	yes	maximal, complemented
3	#10587678	C₂	1	6	yes	maximal, complemented
4	D₁₇⋊M₁₆	C₂	1	3	yes	maximal, complemented
5	C₂×#63243	C₂	1	3	yes	maximal, complemented
6	#41×C₁₇	C₄	1	1	yes	characteristic
7	#63256	C₂²	1	1	yes	characteristic
8	Q₈×D₁₇	C₄	1	1	yes	characteristic
9	#63254	C₂²	1	3	yes	—
10	D₄×D₁₇	C₄	1	3	yes	—
11	#63252	C₄	1	3	yes	—
12	C₂×C₄×D₁₇	C₂²	1	3	yes	—
13	#63247	C₂²	1	6	yes	complemented
14	C₂×#3624	C₂²	1	6	yes	complemented
15	#63243	C₂²	1	3	yes	—
16	#63243	C₂²	1	1	yes	characteristic
17	#63243	C₂²	1	6	yes	complemented
18	#63242	C₂²	1	6	yes	complemented
19	C₂²×D₁₇	C₂×C₄	1	3	yes	—
20	Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
21	D₄×C₁₇	C₂×C₄	1	3	yes	—
22	C₂×C₄×C₁₇	C₂×C₄	1	3	yes	—
23	C₂²⋊D₁₇	C₂×C₄	1	6	yes	—
24	C₂×Dic₁₇	C₂³	1	3	yes	—
25	D₆₈	C₂×C₄	1	3	yes	—
26	C₄×D₁₇	C₂×C₄	1	3	yes	—
27	C₄×D₁₇	C₂×C₄	1	3	yes	—
28	C₄×D₁₇	C₂³	1	3	yes	—
29	C₄×D₁₇	C₂³	1	1	yes	characteristic
30	Dic₃₄	C₂×C₄	1	3	yes	—
31	#3624	C₂³	1	2	yes	—
32	#3624	C₂³	1	6	yes	—
33	C₂²×C₁₇	C₂²×C₄	1	3	yes	—
34	C₂×D₁₇	—	4	3	no	—
35	C₂×D₁₇	C₂²×C₄	1	1	yes	characteristic
36	C₂×D₁₇	C₂²×C₄	1	3	yes	—
37	C₄×C₁₇	C₂²×C₄	1	3	yes	—
38	C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
39	Dic₁₇	C₂²×C₄	1	3	yes	—
40	Dic₁₇	C₂⁴	1	1	yes	characteristic
41	#568	—	17	1	no	maximal, Sylow
42	C₂×C₁₇	—	2	3	no	—
43	C₂×C₁₇	C₂³×C₄	1	1	yes	characteristic
44	D₁₇	—	2	1	no	—
45	D₁₇	—	2	3	no	—
46	C₂×#41	—	17	1	no	—
47	#131	—	17	6	no	—
48	#131	—	17	2	no	—
49	C₂×M₁₆	—	17	3	no	—
50	C₂×M₁₆	—	17	3	no	—
51	C₁₇	#568	1	1	yes	characteristic, complemented, Sylow
52	#41	—	17	1	no	—
53	#41	—	17	3	no	—
54	#41	—	17	3	no	—
55	#41	#595	1	1	yes	characteristic
56	C₂×Q₈	—	17	1	no	—
57	C₂×D₄	—	17	3	no	—
58	C₂²×C₄	—	17	3	no	—
59	M₁₆	—	17	3	no	—
60	M₁₆	—	17	1	no	—
61	M₁₆	—	17	6	no	—
62	M₁₆	—	17	6	no	—
63	C₂×C₈	—	17	6	no	—
64	C₂×C₈	—	17	6	no	—
65	C₂³	—	17	3	no	—
66	Q₈	—	17	3	no	—
67	Q₈	C₂×#595	1	1	yes	characteristic
68	D₄	—	17	6	no	—
69	D₄	—	17	3	no	—
70	D₄	C₂×#595	1	3	yes	—
71	C₂×C₄	—	17	3	no	—
72	C₂×C₄	—	17	3	no	—
73	C₂×C₄	—	17	1	no	—
74	C₂×C₄	—	17	3	no	—
75	C₂×C₄	—	17	3	no	—
76	C₂×C₄	C₂×#595	1	3	yes	—
77	C₈	—	17	2	no	—
78	C₈	—	17	6	no	—
79	C₂²	—	17	1	no	—
80	C₂²	—	17	3	no	—
81	C₂²	—	68	3	no	—
82	C₂²	C₂²×#595	1	3	yes	—
83	C₄	—	17	1	no	—
84	C₄	—	17	3	no	—
85	C₄	C₂²×#595	1	1	yes	characteristic
86	C₄	C₂²×#595	1	3	yes	—
87	C₂	—	2	3	no	—
88	C₂	—	34	1	no	—
89	C₂	—	34	3	no	—
90	C₂	C₂³×#595	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×#595
commutator, socle	C₂×C₁₇	C₂³×C₄
Fitting	#41×C₁₇	C₄
prime radical	#41×D₁₇	C₂
cosocle	Dic₁₇	C₂⁴
hypercenter	#41	#595
hypocenter	C₁₇	#568
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ #41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #10587680	C₂	semidirect
3. #10587678	C₂	semidirect
4. D₁₇⋊M₁₆	C₂	semidirect
5. C₂×#63243	C₂	semidirect
13. #63247	C₂²	semidirect
14. C₂×#3624	C₂²	semidirect
17. #63243	C₂²	semidirect
18. #63242	C₂²	semidirect
51. C₁₇	#568	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#41×D₁₇	2
#10587680	2
#10587678	2
D₁₇⋊M₁₆	2
C₂×#63243	2
#568	17